Algebra Examples

${(x - 4)}^{2} - \frac{2}{3} = 6 y - 12$

Step 1

Move all terms not containing $x$ to the right side of the equation.

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Step 1.1

Add $\frac{2}{3}$ to both sides of the equation.

${(x - 4)}^{2} = 6 y - 12 + \frac{2}{3}$

Step 1.2

To write $- 12$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

${(x - 4)}^{2} = 6 y - 12 \cdot \frac{3}{3} + \frac{2}{3}$

Step 1.3

Combine $- 12$ and $\frac{3}{3}$ .

${(x - 4)}^{2} = 6 y + \frac{- 12 \cdot 3}{3} + \frac{2}{3}$

Step 1.4

Combine the numerators over the common denominator.

${(x - 4)}^{2} = 6 y + \frac{- 12 \cdot 3 + 2}{3}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 12$ by $3$ .

${(x - 4)}^{2} = 6 y + \frac{- 36 + 2}{3}$

Step 1.5.2

Add $- 36$ and $2$ .

${(x - 4)}^{2} = 6 y + \frac{- 34}{3}$

Step 1.6

Move the negative in front of the fraction.

${(x - 4)}^{2} = 6 y - \frac{34}{3}$

Step 2

Factor.

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Step 2.1

Factor $2$ out of $6 y - \frac{34}{3}$ .

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Step 2.1.1

Factor $2$ out of $6 y$ .

${(x - 4)}^{2} = 2 (3 y) - \frac{34}{3}$

Step 2.1.2

Factor $2$ out of $- \frac{34}{3}$ .

${(x - 4)}^{2} = 2 (3 y) + 2 (- \frac{17}{3})$

Step 2.1.3

Factor $2$ out of $2 (3 y) + 2 (- \frac{17}{3})$ .

${(x - 4)}^{2} = 2 (3 y - \frac{17}{3})$

Step 2.2

To write $3 y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

${(x - 4)}^{2} = 2 (3 y \cdot \frac{3}{3} - \frac{17}{3})$

Step 2.3

Combine $3 y$ and $\frac{3}{3}$ .

${(x - 4)}^{2} = 2 (\frac{3 y \cdot 3}{3} - \frac{17}{3})$

Step 2.4

Combine the numerators over the common denominator.

${(x - 4)}^{2} = 2 \frac{3 y \cdot 3 - 17}{3}$

Step 2.5

Multiply $3$ by $3$ .

${(x - 4)}^{2} = 2 \frac{9 y - 17}{3}$

Step 2.6

Reorder terms.

${(x - 4)}^{2} = 2 (\frac{1}{3} (9 y - 17))$

Step 2.7

Remove parentheses.

${(x - 4)}^{2} = 2 (\frac{1}{3}) (9 y - 17)$